Chapter 6

Question 1

As sample size __, shape of distribution become more like __ curve.

Answer 1

increases,

normal

Question 2

Larger samples show more clear n__ c__ and d__.

Answer 2

Normal Curves,

Distributions

Question 3

Examples of normally distributed variables:

• h__
• w__
• i_
• r__ t__

N__( c__) variables CAN’T be normally distributed.

Answer 3

height
weight
IQ
reaction time 
nominal (categorical)

Question 4

Normal Curve:
Specific b__-shaped curve that is u__, s__, and defined m__.
-Describes the distributions of m__ variables.

-As the size of a s__ approaches the size of the p__, the distribution resembles a normal curve (as long as the population is n__ d__).

Answer 4

bell-shaped, unimodal, symmetric, mathematically.

many

sample, population
normally distributed

Question 5

Standardization: allows for fair c__ when variables are on different s__.

• comparing z-scores: number of s__ d__ a score is from the m__.
• z distribution: n__ distribution of s__ scores.

Answer 5

comparisons, scales
standard deviations, mean
normal, standardized

Question 6

A z score is the number of s__ d__ a particular score is from the m__.

A z score is part of its own distribution, the _ distribution, just as a raw score, such as a person’s height, is part of its own distribution, a distribution of heights.

Answer 6

standard deviations, mean

z

Question 7

Most DV’s are assumed to be __ distributed.

Answer 7

normally

Question 8

If a variable is normally distributed, we can know stuff about l__ of o__.

Answer 8

likelihood, occurence

Question 9

Most stats are based on a__ of n__.

Answer 9

assumption, normality

Question 10

In the Z distribution, the mean is _ and the standard deviation is _.

Answer 10

0, 1

Question 11

Linear Transformations:
-when you add a constant to each score (e.g: x+4)
what happens to the mean?
what happens to the SD?

-when you subtract a constant from each score (e.g: x-6)
what happens to the mean?
what happens to the SD?

-when you divide each score by a constant (e.g. 2)
what happens to the mean?
what happens to the SD?

Answer 11

increases by 4
stays the same

decreases by 6
stays the same

decreases by 1/2
gets smaller by 1/2

Question 12

What is μ

Answer 12

Population Mean (i.e. 0 for z distribution)

Question 13

What is σ

Answer 13

Standard deviation (i.e. 1 for z distribution)

Question 14

To convert RAW scores into their Z scores steps:

• subtract the mean of the __ from the r__ score.
• divide by the s__ d__ of the population.

Practice writing out the equation

Answer 14

population, raw
standard deviation

z= x-μ/σ

Question 15

ex converting raw score into z score:

mean: 6.07
SD: 1.62
raw score: 5

Find the z score.

Answer 15

z= 5-6.07/1.62 = -0.66

Question 16

To convert Z scores into their RAW scores steps:

• multiply the _ score by the _ _ of the population.
• add the __ of the population

Practice writing out the equation

Answer 16

z, SD
mean

x=z∗σ+μ

Question 17

ex converting z score into raw score:

mean: 6.07
SD: 1.62
z score: 1.81

Answer 17

x=1.81∗1.62+6.07 = 9.00

Question 18

If we can standardize raw scores on 2 different scales, by converting both scores to z scores, we can then __ the scores directly.

Answer 18

compare

Question 19

Ex of standardizing two raw scores on different scales:

-Lab A: measured reaction time after 1 drink of alcohol, the population mean was 2.1 seconds, with an SD of 0.3. Larry’s reaction time was 1.4 seconds.

-Lab B: measured reaction times after 2 drinks of alcohol. The population mean was 3.1 seconds, with an SD of 0.6.
Bill’s reaction time was 1.5 seconds.

When using a standardized scale, who has the larger (slower) reaction time?

Answer 19

Larry:

1.4-2.1/0.3 = -2.33

Bill:

1.5-3.1/0.6= -2.67

Larry has the larger Z score and slower time.
-Larry’s score is less negative so LARGER TIME. (larger is longer with time)

Question 20

Transforming Z scores into PERCENTILES:

• z scores tell you __ a values fits into a __ distribution.
• based on a normal distribution, there are rules about where scores with a _ value will fall, and how it will relate to a p__ rank.
• use a__ under normal curve to calculate percentiles for any score.

Answer 20

where, normal

z, percentile

area

Question 21

Break down of percentiles associated with each standard deviation:

DRAW OUT

Answer 21

between 0 and 1/-1—> 34% each side

between 0 and 2/-2—> 14% each side

between 0 and 3/-3—> 2% each side

Question 22

Practice percentile problems:

1) -What percentage falls within 1 standard deviation of the mean?
2) -What percentage falls within 2 standard deviations of the mean?
3) -What percentage is less than the mean?
4) -If you have a raw score equal to z= -1, what is your percentile score?
5) -What is your percentile if z= +1
6) -What is your percentile if z=1.5
7) -What is your percentile if z=0.25
8) -What is your percentile if z= -2.5

Answer 22

1) 34% + 34% = 68%
2) 14+14+34+34=96 OR 100-4=96
3) 50%
4) 16th percentile because you add the percent from -1 and below.
5) 84th percentile
6) 91st percentile
7) 58.5th percentile
8) 1st percentile

Question 23

Practice percentile problems continued:

1) If the pop. has a mean of 125 and std deviation of 10, if you are at the 16th percentile, what would your score be?
2) If your score is 135, what is your percentile?

Answer 23

1) x = -1(10) + 125 = 115
so z = -1
(or just look at chart and where 16% is)

2) z = (135-125)/10 = 1, 84th percentile

Question 24

Check your learning problems:

Check Your Learning

•If the population mean score on a quiz is 10 and the standard deviation is 2:

1) •If a student’s score is 8, what is z?
2) •If a student’s z score is 1.4, what is the raw score?

Answer 24

1) z= -1

2) x=1.4 * 2 +10
=12.8

Question 25

The Central Limit Theorem: -Distribution of s__ means is n__ distributed even when the p__ from which it was drawn is not n__. - A distribution of m__ is less variable then a distribution of i__ scores. - Variability c__.

Answer 25

Sample, normally population, normal means, individual changes

Question 26

The mean of the d__ tends to be the mean of the p__. mean=μ

Answer 26

distribution, population

Question 27

Standard deviation of the d__ tends to be __ than the standard deviation of the p__ of scores.

Answer 27

distribution, less | population

Question 28

What is : M N

Answer 28

M=sample mean N=number of elements in the sample

Question 29

Standard error formula: SD * Population Mean= SD/square root of number of elements in sample The standard error is the standard deviation of the p__ divided by the square root of the sample s__, __. The formula is. Write out in notation.

Answer 29

population size, N σ(M)=σ/√ N

Question 30

Standard Error: s__ d__ of the distribution of m__. -S__ than SD; takes on smaller value as _ increases.

Answer 30

standard deviation, means. smaller, N (number of elements in sample)

Question 31

Write out the Z statistic

Answer 31

z=(M-μ*M)/σM aka z=(sample mean-population mean)/ standard deviation * sample mean

Question 32

The mathematical magic of large samples: -Distribution of m__ follows c__ l__ theorem. The shape of distribution approximates n__ curve IF: - p__ of scores has n__ shape OR - size of each s__ of distribution is n=__+

Answer 32

means, central limit normal population, normal sample, 30+

Question 33

Example calculating the z statistic using population data: A pizza delivery chain claims that it delivers its pizzas to any location within a 15 mile radius within an average of 30 minutes, with a standard deviation of 12 minutes. Suppose a researcher employed by a competitor orders 16 pizzas to be delivered to different locations with a 15 mile radius, and computes a sample mean delivery time of 38 minutes. What is this mean delivery time expressed as a z statistic? Interpret the z statistic. What if sample size was 36?

Answer 33

Standard error: σ/√ N so 12/√16=3 ---> plug into z statistic z statistic: z=(M-μ*M)/σM so z=38-30/3 standard error=12/4= 3 z statistic=38-30/3= 2.67 Thus, the mean delivery time is 2.67 standard errors from the mean. There would be a smaller SD, and the Z statistic would be bigger.